pH and pKa

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  Bases, the other topic in this chapter, are often characterized as cleaning substances that will be discussed later in this chap- ter. In this chapter, we will discuss acids and bases, and expand the concepts of the chemical properties of acids and bases that we introduced in Chapter 15 and apply the principles of chemical equilibrium from Chapter 14 to acids and bases. Using the principles of molecular polarity and the concept of delo- calization of electrons, we were able to qualitatively compare the strengths of acids and bases. Our goal in this chapter is to bring these concepts together as we examine the quantitative aspects of acid–base chemistry. In particular we are interested in acids, bases, and their mixtures as they affect the concen- tration of hydronium ions in solution through the concept of pH. The principles we develop here have applications in laboratories that investigate environmental, forensic, and biochemical problems. High- tech laboratories interested in materials science and nanotechnology often use the principles of acid–base equilibria. The consumer-oriented industries that make products such as cosmetics, foods, beverages, and cleaning chemicals all employ chemists who know that control of pH is very important in safe and effective consumer products. CHAPTER OUTLINE 16.1 Water, pH, and “p” Notation 16.2 pH of Strong Acid and Base Solutions 16.3 Ionization Constants, K a and K b 16.4 Determining K a and K b Values 16.5 pH of Weak Acid and Weak Base Solutions 16.6 Acid–Base Properties of Salt Solutions 16.7 Buffer Solutions 16.8 Polyprotic Acids 16.9 Acid–Base Titrations Acid–Base Equilibria in Aqueous Solutions CHAPTER 16 PIXOLOGICSTUDIO/Getty Images 16.1 Water, pH, and “p” Notation 793 LEARNING OBJECTIVES After reading this chapter and working the problems, you should be able to: • define pH and explain the use of the “p” notation. • explain how to determine the pH of strong acids or bases in aqueous solution.

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  Physicochemical and Biomimetic Properties in Drug Discovery

  Chromatographic Techniques for Lead Optimization

  • Klara Valko(Author)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Chapter 8

  Molecular Physicochemical Properties that Influence Absorption and Distribution—Acid Dissociation Constant—pKa

  Definition of pKa

  The presence of charge on the molecules dramatically influences many of their physicochemical properties, such as lipophilicity, solubility, and permeability. The presence of charge depends on the acid dissociation constant of the ionizable groups and the pH of the solution/environment. The pH is defined as the negative logarithm of the proton or, more precisely, the hydronium ion concentration in aqueous solutions. The product of the concentrations of hydronium and hydroxide ions in water is constant ; thus, the pH normally ranges from 1 to 14. The acid dissociation constant, or , is defined as the pH where an ionizable group is 50% in ionized form. In other words, the acid dissociation constant, , is the equilibrium constant for the reaction in which a weak acid is in equilibrium with its conjugate base in aqueous solution. For example, for acetic acid, the following equilibrium takes place:

  8.1

  8.2

  When the acetate ion concentration is equal to the acetic acid concentration, equals the concentration. The negative logarithm of the concentration is the pH. The smaller the value of , the stronger is the acid. For basic compounds, Equation 8.3 and Equation 8.4 can be used.

  8.3

  8.4

  Again, the negative logarithm of equals the pH of the aqueous environment, where 50% of the basic group is in a protonated charged form, while 50% is in a neutral, unionized form. The percentage of the ionized molecules depends on the proton concentration (pH) and can be calculated at any pH using the Henderson–Hasselbalch equation [1]. Equation 8.5 describes the relationship between the percentage of ionized molecules and pH for a given

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  High-tech laboratories interested in materials science and nanotechnology often use the principles of acid–base equilibria. The consumer-oriented industries that make products such as cosmetics, foods, beverages, and cleaning chemicals all employ chemists who know that control of pH is very important in safe and effective consumer products. LEARNING OBJECTIVES After reading this chapter, you should be able to: • define pH and explain the use of “p” notation • explain how to determine the pH of strong acids or bases in aqueous solution • write expressions for the acid ionization constant, K a , and base ionization constant, K b , and explain how they are related to each other • describe how to determine acid and base ionization constants from experimental data • determine equilibrium concentrations and pH for weak acid or base solutions • explain how a salt solution can be acidic or basic • describe what a buffer solution is, how it works, and how to calculate pH changes in a buffer • define polyprotic acids and describe how to calculate concentrations of all species in a solution of a polyprotic acid • draw and explain titration curves for reactions of strong or weak acids and bases 764 Chapter 16 | Acid–Base Equilibria in Aqueous Solutions Its equilibrium law, following the procedures developed in Section 14.4, is 3 H 3 O + 4 3 OH - 4 = K w (16.1) Since water is a pure liquid, with a constant 55.6 molar concentration, it does not appear in this equilibrium law. Because of the importance of the autoionization equilibrium, its equilibrium constant is given the special symbol, K w , that is called the ion product con- stant of water. Often, for convenience, we omit the water molecule that carries the hydrogen ion and write H + in place of H 3 O + . The equilibrium equation for the autoionization of water then simplifies to H 2 O m H + + OH - The equation for K w based on this is likewise simplified.

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  Analytical Chemistry

  A Toolkit for Scientists and Laboratory Technicians

  • Bryan M. Ham, Aihui MaHam(Authors)
  • 2024(Publication Date)
  • Wiley

    (Publisher)

  The expression used in the analytical laboratory of the acidity or basicity of a solution is the pH of the solution. The pH of a solution is the representation of the molar hydrogen ion concentration [H + ], (M), in solution. Let us spend a moment to consider a little deeper the behavior of acids and bases in solu- tion as systems at equilibrium that will lead us to the definition and calculation of pH. For the dissociation of an acid in aqueous solution, we have the general Equation 9.9: AH acid + H 2 O ⇌ H 3 O + hydronium ion + B − base (9.9) Reactions such as the dissolution of an acid in aqueous solution can be expressed in equation notation as the molar concentration of the products divided by the reactants. This form of expression is equal to the equilibrium constant of the reaction (K c ) and written as such: K c = [H 3 O + ][A − ] [AH][H 2 O] (9.10) The molar concentration of water, [H 2 O], in solutions that are dilute acids or bases is always 55.51 M, so the equilibrium equation can be written as K c = [H 3 O + ][A − ] [AH](55.51) (9.11) 9.7 THE ACID IONIZATION CONSTANT We can now derive what is known as the acid ionization constant, K a , for a general acid in aqueous solution (after substituting [H + ] in the place of [H 3 O + ]): K c × 55.51 = [H + ][A − ] [AH] = K a (9.12) Since the molar concentration of water has been incorporated into the ionization constant, the dissolution of an acid in aqueous solution is usually written without H 2 O as: AH ⇌ H + + A − (9.13) For the dissolution of HCl acid in aqueous solution: HCl ⇌ H + + Cl − (9.14) The expression for the acid ionization constant is K a = [H + ][Cl − ] [HCl] (9.15) Table 9.1 lists some common acid ionization constants (K a ). As a general guideline, if K a is greater than 1 × 10 3 then the acid is very strong; if K a is between 1 × 10 3 and 1 × 10 −2 then the acid is strong; if K a is between 1 × 10 −2 and 1 × 10 −7 the acid is weak; and if the K a is less than 1 × 10 −7 the acid is very weak.

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  Chemistry

  The Molecular Nature of Matter

  • James E. Brady, Neil D. Jespersen, Alison Hyslop(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  According to the color code, the pH of the solution is closer to 3 than to the color for pH 5. Andy Washnik 806 Chapter 16 | Acid–Base Equilibria in Aqueous Solutions | Summary Organized by Learning Objective Define pH and explain the use of “p” notation Water reacts with itself to produce small amounts of H 3 O + (often abbreviated H + ) and OH - ions. The concentrations of these ions, both in pure water and dilute aqueous solutions, are related by the expression 3 H + 4 3 OH - 4 = K w = 1.0 Ž 10 -14 (at 25 °C) K w is the ion product constant of water. In pure water 3 H + 4 = 3 OH - 4 = 1.0 Ž 10 -7 The pH of a solution is defined by the equation, pH = -log[H + ]. As the pH decreases, the acidity, or [H + ], increases. The compa- rable term, pOH (= -log[OH - ]), is used to describe a solution that is basic. A solution is acidic if the hydrogen ion concentration exceeds 1.0 Ž 10 -7 or the pH is less than 7.00. Similarly, a solution is basic if the hydroxide ion concentration exceeds 1.0 Ž 10 -7 or if the pH is greater than 7.00. Explain how to determine the pH of strong acids or bases in aqueous solution When calculating the pH of strong acids or strong bases, we assume that they are 100% ionized. Write expressions for the acid ionization constant, K a , and base ionization constant, K b , and explain how they are related to each other A weak acid H A ionizes according to the general equation H A + H 2 O m H 3 O + + A - or more simply, H A mH + + A - The equilibrium constant is called the acid ionization con- stant, K a : K a = 3 H 3 O + 4 3 A - 4 3 H A 4 A weak base B ionizes by the general equation B + H 2 O mBH + + OH - The equilibrium constant is called the base ionization con- stant, K b : K b = 3 BH + 4 3 OH - 4 3 B 4 The smaller the values of K a (or K b ), the weaker are the sub- stances as Brønsted acids (or bases).

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  General, Organic, and Biological Chemistry

  An Integrated Approach

  • Kenneth W. Raymond(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  An approach to use for determining the concentration of an unknown acid is shown here. ■ Titration is used to determine the concentration of an unknown acid or base solution. 7.9 Effect of pH on Acid and Conjugate Base Concentrations 259 7.9 EFFECT OF pH ON ACID AND CONJUGATE BASE CONCENTRATIONS Some of the compounds important to living things are acids. Whether they are found in their acid or conjugate base form depends on the pH. We have seen that K a and pK a provide information about the relative concentrations of products and reactants in acid–base reactions. For example, the K a for HF is 6.6 * 10 -4 (pK a = 3.18), so at equilibrium, the concentration of HF is greater than the product of the concentrations of F - and H 3 O + . HF + H 2 O N F - + H 3 O + K a = [F - ][H 3 O + ] [HF] = 6.6 * 10 -4 ; pK a = 3.18 We have also seen that Le Châtelier’s principle allows us to predict how changing the concentration of a reactant or product will be followed by a change in the rate of the for- ward or reverse reaction as equilibrium is reestablished. For the reaction above, increasing the concentration of H 3 O + (lowering the pH) will cause the reverse reaction to speed up, which consumes F - and produces HF. Reducing the concentration of H 3 O + (raising the pH) will cause the forward reaction to speed up, which consumes HF and produces F - . Thus, the relative amounts of HF and F - present in a solution depend on the pH. An interesting relationship exists between pH and the relative concentrations of an acid and its conjugate base: • When the pH is adjusted to have the same value as the pK a (pH = pK a ), the concentration of acid equals the concentration of its conjugate base. For the acid HF (pK a = 3.18), this means that [HF] = [F - ] when the pH is 3.18 (Table 7.6). STRATEGY Calculating the concentration of the HCl solution involves determining the number of moles of HCl present in the initial 75 mL of solution.

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  Visualizing Everyday Chemistry

  • Douglas P. Heller, Carl H. Snyder(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  [H 3 O + ] [H 3 O + ] A basic solution has a pH greater than 7. 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 Low concentration High concentration Low concentration High concentration pH = 3 Here, [H 3 O + ] = 10 –3 , so pH = 3. [H 3 O + ] [H 3 O + ] [OH – ] An acidic solution has a pH less than 7. 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 10 –14 10 –13 10 –12 10 –11 10 –10 10 –9 10 –8 10 –7 10 –6 10 –5 10 –4 10 –3 10 –2 10 –1 10 0 Low concentration High concentration Low concentration High concentration [OH – ] Any increase in the hydronium ion concentration above 10 −7 (with an associated decrease in the hydroxide ion concentration) produces an acidic solution: Any decrease in the hydronium ion concentration below 10 −7 (with an associated increase in the hydroxide ion concentration) produces a basic solution: The pH Scale 245 increases [OH − ] and lowers [H 3 O + ]. We can see this see- saw effect and its relation to pH in Figure 8.11 In Words, Math, and Pictures. To summarize, at 25°C: • The pH of a neutral solution equals 7. • The pH of an acidic solution is less than 7. • The pH of a basic solution is greater than 7. We can see the relationship between hydronium ion con- centration and pH in Figure 8.12. We can increase the H 3 O + concentration of a solution by adding acid, such as HCl. Conversely, we can increase the OH − concentration by adding base, such as NaOH. Furthermore, the value obtained by multiplying the hy- dronium ion concentration of a solution, [H 3 O + ], by its hydroxide ion concentration, [OH − ], is always constant, regardless of the addition of acid or base to the water. Since the value of this product remains fixed at any spe- cific temperature, adding acid not only increases [H 3 O + ] but lowers [OH − ] as well.

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  Basic Physical Chemistry for the Atmospheric Sciences

  • Peter V. Hobbs(Author)
  • 2000(Publication Date)
  • Cambridge University Press

    (Publisher)

  We see from definition (5.14) that (1) the greater the hydrogen ion concentration (i.e., the more acidic the solution) the smaller is the pH value of the solution, and (2) a change in the hydrogen ion concentration by a factor of ten (e.g., from 10 1 to 10~ 2 M) changes the pH value by unity. At the beginning of this section we defined a solution as being neutral if [H + (aq)] = [OH(aq)]. Pure water is neutral; therefore, from Eqs. (5.12) and (5.13) [H 3 O + (aq)][OH-(aq)] = l(r 14 or, [H 3 O + (aq)] 2 =10-Therefore, for pure water [H 3 O + (aq)] = [H + (aq)] = 10 7 M Hence, the pH of pure water is -log(10~ 7 ) = 7. It follows that acidic solu-tions have pH < 7 and basic solutions have pH > 7. Observed pH values in nature are generally between 4 and 9. Seawater normally has a pH between 8.1 and 8.3. Streams in wet climates generally have a pH between 5 and 6.5 and in dry climates between 7 and 8. Soil water in the presence of abundant decaying vegetation may have a pH of 4 or lower. The pH of rainwater can range from quite acidic (around 4.0) in industrial regions to about 5.6 in very clean regions. We will discuss the acidity of rainwater in some detail at the end of this chapter, but the following exercise illustrates why even clean rainwater does not have a pH of 7. Exercise 5.2. The pH of natural rainwater is about 5.6. Assum-ing that all of this acidity is due to the absorption of CO 2 by the rain, determine how many moles of CO 2 would have to be absorbed in 1L of rainwater. Solution. Since the pH of rainwater is 5.6, the concentration of H 3 O + (aq) in natural rainwater is given by pH = 5.6 = -log[H 3 O + (aq)] Therefore, [H 3 O + (aq)] = 0.25xl0-5 M 90 Acids and bases The main source of H 3 O + (aq) when CO 2 dissolves in water is CO 2 (g) + H 2 O(l)+±H 2 CO 3 (aq) (5.15a) H 2 CO 3 (aq) + H 2 O(1) ?± HCO 3 -(aq) + H 3 O + (aq) (5.15b) We see from Reactions (5.15) that for every mole of CO 2 that is absorbed in water, one mole of H 3 O + (aq) is produced.

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  Analytical Chemistry

  • Gary D. Christian, Purnendu K. Dasgupta, Kevin A. Schug(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  The product of the Chemists (and especially students!) are lucky that nature made K w an even unit number at room temperature. Imagine doing pH calculations with a K w like 2.39 × 10 −13 . However, see Section 7.5 where you must indeed do this for other temperatures. hydrogen ion concentration and the hydroxide ion concentration in aqueous solution is always equal to 1.0 × 10 −14 at room temperature: [H + ] [OH − ] = 1.0 × 10 −14 (7.14) In pure water, then, the concentrations of these two species are equal since there are no other sources of H + or OH − except H 2 O dissociation: [H + ] = [OH − ] Therefore, [H + ][H + ] = 1.0 × 10 −14 [H + ] = 1.0 × 10 −7 M ≡ [OH − ] If an acid is added to water, we can calculate the hydroxide ion concentration if we know the hydrogen ion concentration from the acid. But when the hydrogen ion concentration from the acid is very small, 10 −6 M or less, the contribution to [H + ] from the ionization of water cannot be neglected. Example 7.1 A 1.0 × 10 −3 M solution of hydrochloric acid is prepared. What is the hydroxide ion concentration? Solution Since hydrochloric acid is a strong electrolyte and is completely ionized, the H + concentration is 1.0 × 10 −3 M. Thus, (1.0 × 10 −3 )[OH − ] = 1.0 × 10 −14 [OH − ] = 1.0 × 10 −11 M  7.4 The pH Scale The concentration of H + or OH − in aqueous solution can vary over extremely wide pScales are used to compress and more conveniently express a range of numbers that span several decades in magnitude. ranges, from 1 M or greater to 10 −14 M or less. To construct a plot of H + concentration against some variable would be very difficult if the concentration changed from, say, 10 −1 M to 10 −13 M. This range is common in a titration. It is more convenient to 228 CHAPTER 7 ACID–BASE EQUILIBRIA compress the acidity scale by placing it on a logarithm basis.

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  Analytical Chemistry

  • Gary D. Christian, Purnendu K. Dasgupta, Kevin A. Schug(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  A number, partic- ularly specific enzyme reactions that might be used for analyses (see Chapter 23), may occur in the pH range of 4 to 10 or even outside of this. The proper selection of buffers Pdf _Folio:2 47 248 CHAPTER 6 ACID–BASE EQUILIBRIA for the study of biological reactions or for use in clinical analyses can be critical in determining whether or not they influence the reaction. A buffer must have the correct pK a , near physiological pH so the ratio of [A - ]∕[HA] in the Henderson–Hasselbalch equation is not too far from unity, and it must be physiologically compatible. Phosphate Buffers One useful series of buffers are phosphate buffers. Biological systems usually con- tain some phosphate already, and phosphate buffers will not interfere in many cases. By choosing appropriate mixtures of H 3 PO 4 ∕H 2 PO 4 - , H 2 PO 4 - ∕HPO 4 2- , or HPO 4 2- ∕PO 4 3- , solutions over a wide pH range can be prepared. See G. D. Christian and W. C. Purdy, J. Electroanal. Chem., 3 (1962) 363 for the compositions of a series of phosphate buffers at a constant ionic strength of 0.2. Ionic strength is a mea- sure of the total salt content of a solution (see Chapter 5), and it frequently influences reactions, particularly in kinetic studies. Hence, these buffers could be used in cases where the ionic strength must be constant. However, the buffering capacity decreases markedly as the pH approaches the values for the single salts listed, and the single salts are not buffers at all. The best buffering capacity, obtained at the half neutralization points, is within ±1pH unit of the respective pK a values, that is, 1.96 ± 1, 7.12 ± 1, and 12.32 ± 1. Example 6.24 What weights of NaH 2 PO 4 and Na 2 HPO 4 would be required to prepare 1 L of a buffer solution of pH 7.45 that has an ionic strength of 0.100? Solution Let x = [Na 2 HPO 4 ] and y = [NaH 2 PO 4 ]. There are two unknowns, and two equations are needed.

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